Abstract
This paper addresses the finite-time observer-based control for Markovian jump systems with time-varying generally uncertain transition rates. In order to estimate the states, a suitable observer is designed, in which both external disturbance and Brownian motion exist. In order to solve the complex time-varying transition rates, a quantization mechanism is raised to prove the closed-loop system and the observer error system be stable. Sufficient conditions of the existences of both the observer and the observer-based controller are derived in terms of linear matrix inequalities. Eventually, two practical examples are given to testify the correctness of the results.